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→Boolean function
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== Boolean function == | == Boolean function == | ||
{{Main|Boolean function}} | |||
When the arguments to Equal to are [[Boolean]], it is the [[wikipedia:Logical biconditional|Logical biconditional]] function, or the [[Not|negation]] of the [[xor]] function (which is [[Not Equal to]] restricted to Boolean arguments). This function is also known as xnor or the Kronecker delta. | When the arguments to Equal to are [[Boolean]], it is the [[wikipedia:Logical biconditional|Logical biconditional]] function, or the [[Not|negation]] of the [[xor]] function (which is [[Not Equal to]] restricted to Boolean arguments): | ||
{|class=wikitable | |||
!<source lang=apl inline>≤</source>!!<source lang=apl inline>0</source>!!<source lang=apl inline>1</source> | |||
|- | |||
!<source lang=apl inline>0</source> | |||
|<source lang=apl inline>1</source>||<source lang=apl inline>0</source> | |||
|- | |||
!<source lang=apl inline>1</source> | |||
|<source lang=apl inline>0</source>||<source lang=apl inline>1</source> | |||
|} | |||
In the context of logic, it can be read as ''if and only if''. This function is also known as xnor or the Kronecker delta. | |||
[[Reduction]] with <source lang=apl inline>=</source> is the same as reduction with xor (<source lang=apl inline>≠</source>), but [[Not|inverted]] if the number of reduced elements is even. The left and right [[identity element]] for Boolean <source lang=apl inline>=</source> is 1. | [[Reduction]] with <source lang=apl inline>=</source> is the same as reduction with xor (<source lang=apl inline>≠</source>), but [[Not|inverted]] if the number of reduced elements is even. The left and right [[identity element]] for Boolean <source lang=apl inline>=</source> is 1. | ||